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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Fair Repetitive Interval Scheduling
Klaus Heeger, Danny Hermelin, Yuval Itzhaki, Hendrik Molter, Dvi · 2024-07-04 · via cs.DS updates on arXiv.org

Fair resource allocation is undoubtedly a crucial factor in customer satisfaction in several scheduling scenarios. This is especially apparent in repetitive scheduling models where the same set of clients repeatedly submits jobs on a daily basis. In this paper, we aim to analyze a repetitive scheduling system involving a set of $n$ clients and a set of $m$ days. On every day, each client submits a request to process a job exactly within a specific time interval, which may vary from day to day, modeling the scenario where the scheduling is done Just-In-Time (JIT). The daily schedule is executed on a single machine that can process a single job at a time, therefore it is not possible to schedule jobs with intersecting time intervals. Accordingly, a feasible solution corresponds to sets of jobs with disjoint time intervals, one set per day. We define the quality of service (QoS) that a client receives as the number of executed jobs over the $m$ days period. Our objective is to provide a feasible solution where each client has at least $k$ days where his jobs are processed. We prove that this problem is NP-hard even under various natural restrictions such as identical processing times and day-independent due dates. We also provide efficient algorithms for several special cases and analyze the parameterized tractability of the problem with respect to several parameters, providing both parameterized hardness and tractability results.